PS5 is in transit for next week.
I have the room for practically any TV and permission on the budget up to $10k
I could get the TCL 100p715 for ~$9500 - Seen one today its huge but only HDMI 2.0
Or the Samsung Samsung Q80T 85 for ~$4950 which appears to be the biggest HDMI 2.1 TV but is "only" 85 inchs
Or wait until next year, will there be more larger HDMI 2.1 TV's next year?
While the budget is generous that's it for this decade…
You should check info about "input lag" on each TV before you buy it.
Gaming with a 80ms input lag will surely give a lot of frustration for you.
https://www.rtings.com/tv/tests/inputs/input-lag